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Dynamical response of hyper-elastic cylindrical shells under periodic load

  • Jiu-sheng Ren (任九生)Email author
Article

Abstract

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.

Key words

hyper-elastic cylindrical shells nonlinear differential equation periodic oscillation quasi-periodic oscillation critical load 

Chinese Library Classification

O343 

2000 Mathematics Subject Classification

74B20 

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Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Mechanics, Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China

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